Conventionally, as a stop control system for an internal combustion engine, one disclosed in Patent Literature 1 is known. This engine is equipped with an intake air amount-adjusting valve for adjusting the amount of intake air. Further, in this stop control system, during stoppage of the engine, the intake air amount-adjusting valve is controlled to a predetermined opening degree, whereby the magnitude of negative pressure within an intake passage is adjusted to stop the piston of the engine at a predetermined position suitable for restarting the engine. Specifically, in a process before the engine is stopped, the rotational speed of the engine is detected when the piston passes the compression top dead center, and a predetermined map is searched according to the detected rotational speed at the compression top dead center to thereby set the opening degree of the intake air amount-adjusting valve. This adjusts the rate of reduction of the rotational speed of the engine to stop the piston at the predetermined position, whereby the startability of the engine is improved at the restart thereof.